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# Common Core Standard HSA-REI.D.12 Questions

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

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Do the inequalities $y<-x^2-x$ and $(y+5)^2+x^2<2$ overlap?
1. Yes, they overlap
2. No, they do not overlap
3. No, but they touch
Do the inequalities $y<-3x^2-.1x$ and $y>x^2+2-2$ overlap?
1. Yes, they overlap
2. No, they do not overlap
3. No, but they touch
Do the inequalities $y> x^2+4x+4$ and $y < x-4$ overlap?
1. Yes, they overlap
2. No, they do not overlap
3. No, but they touch
Do the inequalities $y<-x^2+2x+6$ and $y>x^2+2-3$ overlap?
Do the inequalities $y> -3x^2+14x+2$ and $(y+4)^2+(x+5)^2<2$ overlap?